VERIFICATION OF THE CONCLUSIONS OF POSITRON THEORY

At the present time, the attention of a broad circle of physicists is being attracted by the experimental verification of the conclusions of positron theory, both qualitative and, in particular, precise and quantitative.

The state of the question has already been covered in a number of reviews¹ and original papers². At present, however, several new brief communications have appeared that are of considerable interest.

1. Of great importance is the verification of the accuracy of the agreement of the numerical values of \(e\) and \(m\) for electrons and positrons.

As is known, for the charge of the positron \(e^+\) there is at present the value \(e^+ = 4.84 \pm 0.03 \cdot 10^{-10}\), which is not in particularly good agreement with \(e^- = 4.8022 \cdot 10^{-10}\).

In the note under review³ the question of the agreement of the values \(m^+\) and \(m^-\) is discussed.

Taking the most reliable value of the Compton wavelength \(\lambda_k = \dfrac{h}{mc}\), determined by ordinary methods (i.e., for \(e^-\)),

\[ \lambda_k = (2.426067 \pm 0.000032)\times 10^{-10}\ \text{cm}, \]

and comparing it with the value obtained by him in measuring the annihilation \(\lambda\),¹⁴

\[ \lambda_A = (2.4271 \pm 0.0010)\cdot 10^{-10}\ \text{cm}, \]

the author takes in the second case for \(m\) the value

\[ \frac{1}{2}(m^- - m^+). \]

Hence he finds

\[ \frac{m^- - m^+}{m^-} = 0.82 \cdot 10^{-4}, \]

FROM CURRENT LITERATURE

i.e., a value for the positron mass somewhat smaller than for the electron mass (hence—the difference in the ratios \(e/m\) will already be significant!).

Having carefully weighed the possible error of his experiments, the author estimates it as \(\pm 0.00012\); thus, in the author’s opinion, the discrepancy in the values of \(m\) exceeds the experimental error by a factor of 8.

The author considers the graduation of the \(\gamma\)-spectrometer by wavelengths to be the most vulnerable point of his method.

More precise measurements are expected. In work \(^{10}\) the measurement of the annihilation \(\lambda\) was carried out on the basis of the following principle. The \(\gamma\)-radiation of \(\mathrm{Au}^{198}\) (411 kev) underwent conversion on the \(L_{\mathrm{III}}\) levels of uranium atoms; the wavelength of the radiation obtained upon conversion of the annihilation radiation from \(\mathrm{Cu}^{64}\) in the same uranium (\(K\)-level) was compared with the corresponding wavelength; according to theory this wavelength should differ from the first by no more than \(0.001\) of its magnitude.

To refine the radiation energy, a comparison was made of the lines obtained upon conversion of \(\mathrm{Au}^{198}, U_{L_{\mathrm{III}}}\) and \(\mathrm{Co}^{60}, U_K\), as well as \(\mathrm{Au}^{198}, U_K\) and \(\mathrm{Au}^{198}, U_L\).

The experiments gave for the annihilation energy the value \(510.37 \pm 0.14\) kev, whereas the theoretical value is \(m^{-}c^2 = 510.96 \pm 0.02\) kev. The authors suggest that the discrepancy is connected with the fact that \(m^{+} < m^{-}\), and hence find

\[ \frac{m^{-} - m^{+}}{m^{-}} = 23 \cdot 10^{-4}, \]

which is almost 30 times greater than the value obtained by Dumond.

1. As is known, theory predicts the possibility of zero-quantum, one-, two-, and three-quantum annihilation.

The most probable is two-quantum annihilation, which is usually observed; zero-quantum annihilation is very unlikely and has not been reliably observed \(^{5,6}\); the production of one-quantum annihilation in the experiments of Gray and Tarrant is apparently unreliable \(^{3}\). Three-quantum annihilation had not been observed up to this time.

In the note under review \(^{7}\), the observation of three-quantum annihilation is described.

Around the source (\(\mathrm{Cu}^{64}\) from spectroscopically pure copper irradiated with slow neutrons) three crystal counters (naphthalene–anthracene), connected in a coincidence circuit, were arranged symmetrically. The resolving power of the circuit was \(5 \cdot 10^{-7}\). The source was enclosed in an Al jacket, stopping all particles except photons; Pb screens eliminated coincidences due to scattered particles, etc.

Experiments on the absorption of the radiation under study showed that it is softer than the usual radiation in two-quantum annihilation (about \(\sim 0.33\) Mev is expected instead of \(0.51\) Mev).

The author finds the ratio of the probabilities of two- and three-quantum annihilation (depending on assumptions about the sensitivities of the counters to radiations of 0.33 and 0.51 Mev, the ratio of which lies, in the author’s opinion, within the limits from 1 to 1.18) to lie within the limits from \((2.0 \pm 0.4)\cdot 10^3\) to \((3.3 \pm 0.7)\cdot 10^3\).

This ratio agrees fairly well with the predictions of theory: from \(2.35 \cdot 10^3\) to \(3.7 \cdot 10^2\).

V. A. Kizel

CITED LITERATURE

1. Khol’nov, UFN 41, 350 (1950).
2. Vlasov, Izv. AN, ser. fiz. 14, 337 (1950).
3. J. Du Mond, Phys. Rev. 81, 468 (1951).

1. J. Du Mond, Lind, Watson, Phys. Rev. 75, 1226 (1949).
2. Perrin, Comptes Rendus 197, 1302 (1933).
3. Brunnings, Physica 1, 966 (1934).
4. Rich, Phys. Rev. 81, 140 (1951).
5. Lifshits, DAN 60, 211 (1948).
6. Ore and Powell, Phys. Rev. 75, 1696 (1949).
7. Hedgran and Lind, Phys. Rev. 82, 126 (1951).